Multilayer network representation of membrane potential and cytosolic calcium concentration dynamics in beta cells

Abstract

a r t i c l e i n f o a b s t r a c tModern theory of networks has been recognized as a very successful methodological concept for the description and analysis of complex systems. However, some complex systems are more complex than others. For instance, several real-life systems are constituted by interdependent subsystems and their elements are subjected to different types of interactions that can also change with time. Recently, the multilayer network formalism has been proposed as a general theoretical framework for the description and analysis of such multi-dimensional complex systems and is acquiring more and more prominence in terms of a new research direction. In the present study, we use this methodology for the description of functional connectivity patterns and signal propagation between pancreatic beta cells in an islet of Langerhans at the levels of membrane potential (MP) and cytosolic calcium concentration ([Ca 2+ ] c ) dynamics to study the extent of overlap in the two networks and to clarify whether time lags between the two signals in individual cells are in any way dependent on the role these cells play in the functional networks. The two corresponding network layers are constructed on the basis of signal directions and pairwise correlations, whereas the interlayer connections represent the time lag between both measured signals. Our results confirm our previous finding that both MP and [Ca 2+ ] c change spread across an islet in the form of a depolarization and a [Ca 2+ ] c wave, respectively. Both types of waves follow nearly the same path and the networks in both layers have a similar but not entirely the same structure. We show that the observed discrepancies are attributed to variability in delays between the depolarization and rise in [Ca 2+ ] c . In particular, high-degree nodes in both layers are found to exhibit a larger time lag between the MP and the [Ca 2+ ] c signal than nodes with less connections. We speculate that this finding reflects a higher activity of endoplasmic reticulum calcium pumps in the most connected cells. Our findings indicate that visualizing and studying the temporal information flow and interaction patterns between beta cells as a multiplex network can provide valuable new insights into the physiology of the complex signaling processes in islets of Langerhans.

Membrane Potential and Calcium Dynamics in Beta Cells from Mouse Pancreas Tissue Slices: Theory, Experimentation, and Analysis

“…Due to its advantageously-high sensitivity, [Ca 2+ ] i imaging is used most commonly [ 134 ] and was successfully employed to indicate the degree of synchronicity between beta cells in mouse [ 73 , 127 , 135 , 136 , 137 ] and human islets [ 83 , 103 , 138 , 139 , 140 , 141 , 142 ]. Recently, data on [Ca 2+ ] i dynamics in mice provided valuable novel insight into the physiology of beta cells [ 78 , 79 , 80 , 81 , 87 ]. However, since beta cell stimulus-secretion coupling is complex in the sense that it involves many additional steps upstream and downstream from changes in [Ca 2+ ] i , deducing the whole signaling from the input in the form of glucose and other nutrients to the output in the form of insulin secretion by analyzing changes in [Ca 2+ ] i only is not possible.…”

“…Furthermore, in every cell, the increase in MP typically precedes the increase in [Ca 2+ ] i by >100 ms [ 86 ]. Finally, a multilayer network representation and analysis of the MP and [Ca 2+ ] i signal propagation assessed in mice by means of our double stain paradigm showed that the largest delays between the MP and the [Ca 2+ ] i signal are present in the most connected cells in the tissue [ 80 ]. This observation can be a consequence of various reasons that are principally related with the well-known heterogeneity of beta cells [ 60 , 65 ].…”

“…More specifically, a higher number of cytosolic buffers in larger cells would evoke a slower rise in [Ca 2+ ] i . Alternatively, the slower rise could be a consequence of more active pumping into the ER and out of the cells, which has recently been suggested by the higher energy consumption found in the most connected cells [ 80 ]. These properties remained undiscovered in previous studies on cell lines [ 148 ] and isolated islets [ 150 ].…”

“…Moreover, recently we and others studied populations of beta cells by means of graph-theoretical approaches and, thereby, succeeded in showing that the beta cells form a complex network [ 78 ]. The extracted non-trivial topological features importantly determine the heterogeneity of individual cells [ 79 , 80 ], and can be modulated by physiological [ 48 , 81 ] and pathophysiological influences [ 82 , 83 , 84 ].…”

Inter-layer competition in adaptive multiplex network

“…In particular, multiplex networks (the sub-class of multi-layer networks where nodes are the same on all layers) found applications in technological [3][4][5], biological [6], and social systems [7,8], as well as in human brain, artificial intelligence and robotics [9,10]. Multiplex networks are furthermore useful tools for the analysis of climatological data, e.g.…”